grandes-ecoles 2022 Q3.4

grandes-ecoles · France · x-ens-maths-d__mp Groups Subgroup and Normal Subgroup Properties

For all $w\in V$ such that $B(w,w)>0$, define $$s_w : v \mapsto v - 2\frac{B(v,w)}{B(w,w)}w.$$ Show that $s_w \in G_0$.

For all $w\in V$ such that $B(w,w)>0$, define
$$s_w : v \mapsto v - 2\frac{B(v,w)}{B(w,w)}w.$$
Show that $s_w \in G_0$.